Polynommultiplikation
polymult <- function(x,a,b)
# a(B) = a_0 + a_1*B + a_2*B² + ... + a_p*B^p
# b(B) = b_0 + b_1*B + b_2*B² + ... + a_q*B^q
# where wlog p >= q
# Result is a(B)b(B) x_t
{
if (length(b) == 1){polycoeff <- b[1]*array(a)}
else
{alpha <- array(a)
p <- dim(alpha) - 1
beta <- array(b)
q <- dim(beta) - 1
# Assumed: p >= q
polycoeff <- array(rep(0,p+q + 1))
for (k in 0:(p+q))
for (j in max(0,k-q):min(k,p))
{polycoeff[k+1] <- polycoeff[k+1] + alpha[j+1]*beta[k-j+1]}
}
return(filter(x,c(polycoeff),sides=1, method="convolution"))
# test: return(polycoeff)
}
Opstilling af Data
library(readxl)
library(vars)
## Loading required package: MASS
## Loading required package: strucchange
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: sandwich
## Loading required package: urca
## Loading required package: lmtest
library(imputeTS)
## Registered S3 method overwritten by 'xts':
## method from
## as.zoo.xts zoo
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
##
## Attaching package: 'imputeTS'
## The following object is masked from 'package:zoo':
##
## na.locf
library(forecast)
## Warning: package 'forecast' was built under R version 3.6.2
library(tseries)
##
## Attaching package: 'tseries'
## The following object is masked from 'package:imputeTS':
##
## na.remove
library(stats)
library(strucchange)
library(tidyr)
library(astsa)
##
## Attaching package: 'astsa'
## The following object is masked from 'package:forecast':
##
## gas
elprice17 = data.frame(read.csv("elspot-prices_2017_daily_eur.csv",sep=";",dec=","))
cons17= data.frame(read.csv("consumption-se-areas_2017_daily.csv",sep=";"))
prod17 = data.frame(read.csv("production-se-areas_2017_daily.csv",sep=";"))
Price = log(na_interpolation(as.numeric(elprice17[3:367,4]), option = "linear"))
Cons = log(na_interpolation(as.numeric(as.character(cons17[3:367,3])), option = "linear"))
Prod = log(na_interpolation(as.numeric(as.character(prod17[3:367,3])), option = "linear"))
plot.ts(Price)
plot.ts(Cons)
plot.ts(Prod)
acf(Price)
acf(Cons)
acf(Prod)
dato <- seq(c(ISOdate(2017,1,1)), by = "days", length.out = 365)
data1 = data.frame(dato, Price, Cons, Prod)
Prod1= data1[,c(1,4)]
Cons1 = data1[,c(1,3)]
Price1 = data1[,c(1,2)]
Estimation af deterministisk sæson
sprod = glm(Prod1[,2] ~ time(Prod1[,1]) +
I(time(Prod1[,1])^2) +
sin((4*pi)/365*I(time(Prod1[,1])))+
cos((4*pi)/365*I(time(Prod1[,1])))+
sin((8*pi)/365*I(time(Prod1[,1])))+
cos((8*pi)/365*I(time(Prod1[,1])))+
sin((24*pi)/365*I(time(Prod1[,1])))+
cos((24*pi)/365*I(time(Prod1[,1])))+
sin((104*pi)/365*I(time(Prod1[,1])))+
cos((104*pi)/365*I(time(Prod1[,1])))+
sin((730*pi)/365*I(time(Prod1[,1])))+
cos((730*pi)/365*I(time(Prod1[,1])))
)
sprice = glm(Price1[,2] ~ time(Price1[,1]) +
I(time(Price1[,1])^2) +
sin((4*pi)/365*I(time(Price1[,1])))+
cos((4*pi)/365*I(time(Price1[,1])))+
sin((8*pi)/365*I(time(Price1[,1])))+
cos((8*pi)/365*I(time(Price1[,1])))+
sin((24*pi)/365*I(time(Price1[,1])))+
cos((24*pi)/365*I(time(Price1[,1])))+
sin((104*pi)/365*I(time(Price1[,1])))+
cos((104*pi)/365*I(time(Price1[,1])))+
sin((730*pi)/365*I(time(Price1[,1])))+
cos((730*pi)/365*I(time(Price1[,1])))
)
scons = glm(Cons1[,2] ~ time(Cons1[,1]) +
I(time(Cons1[,1])^2) +
sin((4*pi)/365*I(time(Cons1[,1])))+
cos((4*pi)/365*I(time(Cons1[,1])))+
sin((8*pi)/365*I(time(Cons1[,1])))+
cos((8*pi)/365*I(time(Cons1[,1])))+
sin((24*pi)/365*I(time(Cons1[,1])))+
cos((24*pi)/365*I(time(Cons1[,1])))+
sin((104*pi)/365*I(time(Cons1[,1])))+
cos((104*pi)/365*I(time(Cons1[,1])))+
sin((730*pi)/365*I(time(Cons1[,1])))+
cos((730*pi)/365*I(time(Cons1[,1])))
)
summary(sprod)
##
## Call:
## glm(formula = Prod1[, 2] ~ time(Prod1[, 1]) + I(time(Prod1[,
## 1])^2) + sin((4 * pi)/365 * I(time(Prod1[, 1]))) + cos((4 *
## pi)/365 * I(time(Prod1[, 1]))) + sin((8 * pi)/365 * I(time(Prod1[,
## 1]))) + cos((8 * pi)/365 * I(time(Prod1[, 1]))) + sin((24 *
## pi)/365 * I(time(Prod1[, 1]))) + cos((24 * pi)/365 * I(time(Prod1[,
## 1]))) + sin((104 * pi)/365 * I(time(Prod1[, 1]))) + cos((104 *
## pi)/365 * I(time(Prod1[, 1]))) + sin((730 * pi)/365 * I(time(Prod1[,
## 1]))) + cos((730 * pi)/365 * I(time(Prod1[, 1]))))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.44968 -0.08051 0.01333 0.08967 0.32653
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 1.187e+01 2.253e-02 527.138
## time(Prod1[, 1]) -3.242e-03 2.879e-04 -11.262
## I(time(Prod1[, 1])^2) 8.745e-06 7.346e-07 11.905
## sin((4 * pi)/365 * I(time(Prod1[, 1]))) 4.048e-02 1.090e-02 3.715
## cos((4 * pi)/365 * I(time(Prod1[, 1]))) -1.521e-02 1.030e-02 -1.477
## sin((8 * pi)/365 * I(time(Prod1[, 1]))) 1.824e-02 1.023e-02 1.784
## cos((8 * pi)/365 * I(time(Prod1[, 1]))) -2.846e-02 1.001e-02 -2.842
## sin((24 * pi)/365 * I(time(Prod1[, 1]))) -5.563e-03 1.002e-02 -0.555
## cos((24 * pi)/365 * I(time(Prod1[, 1]))) -3.212e-02 9.995e-03 -3.213
## sin((104 * pi)/365 * I(time(Prod1[, 1]))) -8.109e-03 1.000e-02 -0.811
## cos((104 * pi)/365 * I(time(Prod1[, 1]))) -1.009e-01 9.996e-03 -10.097
## sin((730 * pi)/365 * I(time(Prod1[, 1]))) 7.334e+09 1.106e+11 0.066
## cos((730 * pi)/365 * I(time(Prod1[, 1]))) NA NA NA
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## time(Prod1[, 1]) < 2e-16 ***
## I(time(Prod1[, 1])^2) < 2e-16 ***
## sin((4 * pi)/365 * I(time(Prod1[, 1]))) 0.000236 ***
## cos((4 * pi)/365 * I(time(Prod1[, 1]))) 0.140549
## sin((8 * pi)/365 * I(time(Prod1[, 1]))) 0.075320 .
## cos((8 * pi)/365 * I(time(Prod1[, 1]))) 0.004739 **
## sin((24 * pi)/365 * I(time(Prod1[, 1]))) 0.579141
## cos((24 * pi)/365 * I(time(Prod1[, 1]))) 0.001432 **
## sin((104 * pi)/365 * I(time(Prod1[, 1]))) 0.417974
## cos((104 * pi)/365 * I(time(Prod1[, 1]))) < 2e-16 ***
## sin((730 * pi)/365 * I(time(Prod1[, 1]))) 0.947152
## cos((730 * pi)/365 * I(time(Prod1[, 1]))) NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.01822984)
##
## Null deviance: 11.6055 on 364 degrees of freedom
## Residual deviance: 6.4351 on 353 degrees of freedom
## AIC: -412.09
##
## Number of Fisher Scoring iterations: 2
summary(scons)
##
## Call:
## glm(formula = Cons1[, 2] ~ time(Cons1[, 1]) + I(time(Cons1[,
## 1])^2) + sin((4 * pi)/365 * I(time(Cons1[, 1]))) + cos((4 *
## pi)/365 * I(time(Cons1[, 1]))) + sin((8 * pi)/365 * I(time(Cons1[,
## 1]))) + cos((8 * pi)/365 * I(time(Cons1[, 1]))) + sin((24 *
## pi)/365 * I(time(Cons1[, 1]))) + cos((24 * pi)/365 * I(time(Cons1[,
## 1]))) + sin((104 * pi)/365 * I(time(Cons1[, 1]))) + cos((104 *
## pi)/365 * I(time(Cons1[, 1]))) + sin((730 * pi)/365 * I(time(Cons1[,
## 1]))) + cos((730 * pi)/365 * I(time(Cons1[, 1]))))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.204789 -0.043860 0.003861 0.044519 0.236736
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 1.123e+01 1.119e-02 1004.281
## time(Cons1[, 1]) -7.021e-03 1.430e-04 -49.108
## I(time(Cons1[, 1])^2) 1.691e-05 3.648e-07 46.347
## sin((4 * pi)/365 * I(time(Cons1[, 1]))) -2.616e-02 5.411e-03 -4.834
## cos((4 * pi)/365 * I(time(Cons1[, 1]))) -2.665e-02 5.114e-03 -5.211
## sin((8 * pi)/365 * I(time(Cons1[, 1]))) -1.762e-02 5.079e-03 -3.470
## cos((8 * pi)/365 * I(time(Cons1[, 1]))) -9.944e-03 4.973e-03 -2.000
## sin((24 * pi)/365 * I(time(Cons1[, 1]))) -8.262e-04 4.976e-03 -0.166
## cos((24 * pi)/365 * I(time(Cons1[, 1]))) -6.038e-03 4.964e-03 -1.216
## sin((104 * pi)/365 * I(time(Cons1[, 1]))) -2.717e-03 4.966e-03 -0.547
## cos((104 * pi)/365 * I(time(Cons1[, 1]))) -4.006e-02 4.964e-03 -8.070
## sin((730 * pi)/365 * I(time(Cons1[, 1]))) 1.251e+11 5.491e+10 2.278
## cos((730 * pi)/365 * I(time(Cons1[, 1]))) NA NA NA
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## time(Cons1[, 1]) < 2e-16 ***
## I(time(Cons1[, 1])^2) < 2e-16 ***
## sin((4 * pi)/365 * I(time(Cons1[, 1]))) 2.00e-06 ***
## cos((4 * pi)/365 * I(time(Cons1[, 1]))) 3.21e-07 ***
## sin((8 * pi)/365 * I(time(Cons1[, 1]))) 0.000585 ***
## cos((8 * pi)/365 * I(time(Cons1[, 1]))) 0.046306 *
## sin((24 * pi)/365 * I(time(Cons1[, 1]))) 0.868234
## cos((24 * pi)/365 * I(time(Cons1[, 1]))) 0.224641
## sin((104 * pi)/365 * I(time(Cons1[, 1]))) 0.584693
## cos((104 * pi)/365 * I(time(Cons1[, 1]))) 1.11e-14 ***
## sin((730 * pi)/365 * I(time(Cons1[, 1]))) 0.023312 *
## cos((730 * pi)/365 * I(time(Cons1[, 1]))) NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.004495528)
##
## Null deviance: 13.6568 on 364 degrees of freedom
## Residual deviance: 1.5869 on 353 degrees of freedom
## AIC: -923.08
##
## Number of Fisher Scoring iterations: 2
summary(sprice)
##
## Call:
## glm(formula = Price1[, 2] ~ time(Price1[, 1]) + I(time(Price1[,
## 1])^2) + sin((4 * pi)/365 * I(time(Price1[, 1]))) + cos((4 *
## pi)/365 * I(time(Price1[, 1]))) + sin((8 * pi)/365 * I(time(Price1[,
## 1]))) + cos((8 * pi)/365 * I(time(Price1[, 1]))) + sin((24 *
## pi)/365 * I(time(Price1[, 1]))) + cos((24 * pi)/365 * I(time(Price1[,
## 1]))) + sin((104 * pi)/365 * I(time(Price1[, 1]))) + cos((104 *
## pi)/365 * I(time(Price1[, 1]))) + sin((730 * pi)/365 * I(time(Price1[,
## 1]))) + cos((730 * pi)/365 * I(time(Price1[, 1]))))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.4750 -0.4025 0.1499 0.5555 1.3704
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 5.063e+00 1.371e-01 36.936
## time(Price1[, 1]) -5.554e-03 1.752e-03 -3.170
## I(time(Price1[, 1])^2) 1.726e-05 4.471e-06 3.860
## sin((4 * pi)/365 * I(time(Price1[, 1]))) 3.042e-01 6.631e-02 4.588
## cos((4 * pi)/365 * I(time(Price1[, 1]))) -1.958e-01 6.267e-02 -3.125
## sin((8 * pi)/365 * I(time(Price1[, 1]))) -1.405e-02 6.224e-02 -0.226
## cos((8 * pi)/365 * I(time(Price1[, 1]))) -1.375e-01 6.094e-02 -2.256
## sin((24 * pi)/365 * I(time(Price1[, 1]))) 8.059e-02 6.098e-02 1.322
## cos((24 * pi)/365 * I(time(Price1[, 1]))) -1.240e-02 6.083e-02 -0.204
## sin((104 * pi)/365 * I(time(Price1[, 1]))) -3.065e-02 6.086e-02 -0.504
## cos((104 * pi)/365 * I(time(Price1[, 1]))) -3.848e-01 6.083e-02 -6.326
## sin((730 * pi)/365 * I(time(Price1[, 1]))) -9.109e+10 6.729e+11 -0.135
## cos((730 * pi)/365 * I(time(Price1[, 1]))) NA NA NA
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## time(Price1[, 1]) 0.001656 **
## I(time(Price1[, 1])^2) 0.000135 ***
## sin((4 * pi)/365 * I(time(Price1[, 1]))) 6.22e-06 ***
## cos((4 * pi)/365 * I(time(Price1[, 1]))) 0.001928 **
## sin((8 * pi)/365 * I(time(Price1[, 1]))) 0.821594
## cos((8 * pi)/365 * I(time(Price1[, 1]))) 0.024676 *
## sin((24 * pi)/365 * I(time(Price1[, 1]))) 0.187161
## cos((24 * pi)/365 * I(time(Price1[, 1]))) 0.838569
## sin((104 * pi)/365 * I(time(Price1[, 1]))) 0.614818
## cos((104 * pi)/365 * I(time(Price1[, 1]))) 7.64e-10 ***
## sin((730 * pi)/365 * I(time(Price1[, 1]))) 0.892398
## cos((730 * pi)/365 * I(time(Price1[, 1]))) NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.6751302)
##
## Null deviance: 297.25 on 364 degrees of freedom
## Residual deviance: 238.32 on 353 degrees of freedom
## AIC: 906.23
##
## Number of Fisher Scoring iterations: 2
sprod_res = as.ts(sprod$residuals)
sprice_res = as.ts(sprice$residuals)
scons_res = as.ts(scons$residuals)
acf2(sprod_res)
## ACF PACF
## [1,] 0.49 0.49
## [2,] 0.24 0.01
## [3,] 0.31 0.24
## [4,] 0.23 -0.01
## [5,] 0.06 -0.10
## [6,] 0.12 0.11
## [7,] 0.30 0.24
## [8,] 0.05 -0.26
## [9,] -0.03 0.02
## [10,] 0.12 0.07
## [11,] 0.10 0.02
## [12,] -0.03 -0.04
## [13,] 0.03 0.02
## [14,] 0.21 0.13
## [15,] -0.03 -0.18
## [16,] -0.09 -0.01
## [17,] 0.05 0.02
## [18,] -0.02 -0.08
## [19,] -0.14 -0.03
## [20,] -0.13 -0.12
## [21,] -0.01 0.02
## [22,] -0.23 -0.17
## [23,] -0.31 -0.10
## [24,] -0.19 -0.07
## [25,] -0.17 0.04
## [26,] -0.27 -0.08
## [27,] -0.21 -0.02
## [28,] -0.06 0.00
## [29,] -0.26 -0.14
## [30,] -0.33 -0.08
acf2(sprice_res)
## ACF PACF
## [1,] 0.53 0.53
## [2,] 0.17 -0.16
## [3,] 0.16 0.20
## [4,] 0.12 -0.06
## [5,] 0.04 0.00
## [6,] 0.11 0.14
## [7,] 0.20 0.09
## [8,] 0.04 -0.16
## [9,] -0.01 0.08
## [10,] 0.09 0.06
## [11,] 0.08 -0.02
## [12,] 0.01 -0.01
## [13,] 0.04 0.03
## [14,] 0.07 -0.01
## [15,] -0.04 -0.06
## [16,] -0.02 0.05
## [17,] 0.03 -0.04
## [18,] -0.04 -0.06
## [19,] -0.10 -0.03
## [20,] -0.04 0.02
## [21,] -0.02 -0.04
## [22,] -0.14 -0.10
## [23,] -0.15 -0.04
## [24,] -0.13 -0.08
## [25,] -0.13 0.03
## [26,] -0.09 0.01
## [27,] -0.07 -0.07
## [28,] -0.10 -0.03
## [29,] -0.15 -0.02
## [30,] -0.16 -0.09
acf2(scons_res)
## ACF PACF
## [1,] 0.61 0.61
## [2,] 0.40 0.04
## [3,] 0.31 0.07
## [4,] 0.20 -0.03
## [5,] 0.13 -0.01
## [6,] 0.17 0.13
## [7,] 0.26 0.18
## [8,] 0.21 -0.07
## [9,] 0.19 0.03
## [10,] 0.19 0.03
## [11,] 0.12 -0.04
## [12,] 0.00 -0.12
## [13,] 0.00 0.03
## [14,] 0.05 0.06
## [15,] 0.00 -0.07
## [16,] 0.02 0.02
## [17,] 0.03 -0.05
## [18,] 0.01 0.01
## [19,] -0.02 0.01
## [20,] -0.03 -0.03
## [21,] 0.01 0.05
## [22,] -0.01 -0.01
## [23,] 0.01 0.04
## [24,] 0.09 0.09
## [25,] 0.08 -0.01
## [26,] 0.04 -0.03
## [27,] 0.00 -0.06
## [28,] 0.03 0.08
## [29,] -0.06 -0.15
## [30,] -0.08 -0.02
Estimation og valg af SARMA for Pris
acf2(sprice_res)
## ACF PACF
## [1,] 0.53 0.53
## [2,] 0.17 -0.16
## [3,] 0.16 0.20
## [4,] 0.12 -0.06
## [5,] 0.04 0.00
## [6,] 0.11 0.14
## [7,] 0.20 0.09
## [8,] 0.04 -0.16
## [9,] -0.01 0.08
## [10,] 0.09 0.06
## [11,] 0.08 -0.02
## [12,] 0.01 -0.01
## [13,] 0.04 0.03
## [14,] 0.07 -0.01
## [15,] -0.04 -0.06
## [16,] -0.02 0.05
## [17,] 0.03 -0.04
## [18,] -0.04 -0.06
## [19,] -0.10 -0.03
## [20,] -0.04 0.02
## [21,] -0.02 -0.04
## [22,] -0.14 -0.10
## [23,] -0.15 -0.04
## [24,] -0.13 -0.08
## [25,] -0.13 0.03
## [26,] -0.09 0.01
## [27,] -0.07 -0.07
## [28,] -0.10 -0.03
## [29,] -0.15 -0.02
## [30,] -0.16 -0.09
seas_sprice_res1 = sarima(sprice_res,3,0,0,1,0,0,7, no.constant = TRUE);
## initial value -0.205739
## iter 2 value -0.329456
## iter 3 value -0.412408
## iter 4 value -0.422958
## iter 5 value -0.425715
## iter 6 value -0.425722
## iter 7 value -0.425722
## iter 7 value -0.425722
## iter 7 value -0.425722
## final value -0.425722
## converged
## initial value -0.433484
## iter 2 value -0.433492
## iter 3 value -0.433492
## iter 3 value -0.433492
## iter 3 value -0.433492
## final value -0.433492
## converged
seas_sprice_res2 = sarima(sprice_res,2,0,0,1,0,0,7, no.constant = TRUE);
## initial value -0.206984
## iter 2 value -0.355555
## iter 3 value -0.409459
## iter 4 value -0.414653
## iter 5 value -0.414788
## iter 6 value -0.414788
## iter 7 value -0.414788
## iter 7 value -0.414788
## iter 7 value -0.414788
## final value -0.414788
## converged
## initial value -0.421343
## iter 2 value -0.421358
## iter 3 value -0.421358
## iter 3 value -0.421358
## iter 3 value -0.421358
## final value -0.421358
## converged
seas_sprice_res3 = sarima(sprice_res,4,0,0,1,0,0,7, no.constant = TRUE);
## initial value -0.206440
## iter 2 value -0.305208
## iter 3 value -0.409103
## iter 4 value -0.421271
## iter 5 value -0.427345
## iter 6 value -0.428170
## iter 7 value -0.428190
## iter 8 value -0.428190
## iter 8 value -0.428190
## iter 8 value -0.428190
## final value -0.428190
## converged
## initial value -0.435278
## iter 2 value -0.435301
## iter 3 value -0.435301
## iter 4 value -0.435301
## iter 4 value -0.435301
## iter 4 value -0.435301
## final value -0.435301
## converged
seas_sprice_res4 = sarima(sprice_res,3,0,0,2,0,0,7, no.constant = TRUE);
## initial value -0.203956
## iter 2 value -0.326430
## iter 3 value -0.412469
## iter 4 value -0.423640
## iter 5 value -0.426529
## iter 6 value -0.426565
## iter 7 value -0.426567
## iter 8 value -0.426567
## iter 8 value -0.426567
## iter 8 value -0.426567
## final value -0.426567
## converged
## initial value -0.435801
## iter 2 value -0.435814
## iter 3 value -0.435814
## iter 4 value -0.435814
## iter 4 value -0.435814
## iter 4 value -0.435814
## final value -0.435814
## converged
seas_sprice_res5 = sarima(sprice_res,3,0,0,0,0,0,7, no.constant = TRUE);
## initial value -0.210262
## iter 2 value -0.312482
## iter 3 value -0.391609
## iter 4 value -0.406578
## iter 5 value -0.408806
## iter 6 value -0.408817
## iter 6 value -0.408817
## iter 6 value -0.408817
## final value -0.408817
## converged
## initial value -0.410536
## iter 2 value -0.410539
## iter 3 value -0.410540
## iter 4 value -0.410540
## iter 4 value -0.410540
## iter 4 value -0.410540
## final value -0.410540
## converged
seas_sprice_res1$AIC
## [1] 0.1526423
seas_sprice_res2$AIC
## [1] 0.1713686
seas_sprice_res3$AIC
## [1] 0.1544827
seas_sprice_res4$AIC
## [1] 0.1532696
seas_sprice_res5$AIC
## [1] 0.1939803
Estimation og valg af SARMA for Forbrug
seas_scons_res1 = sarima(scons_res,1,0,0,1,0,0,7, no.constant = TRUE)
## initial value -2.731571
## iter 2 value -3.000725
## iter 3 value -3.002720
## iter 4 value -3.002761
## iter 5 value -3.002772
## iter 5 value -3.002772
## iter 5 value -3.002772
## final value -3.002772
## converged
## initial value -2.987264
## iter 2 value -2.987335
## iter 3 value -2.987335
## iter 3 value -2.987335
## iter 3 value -2.987335
## final value -2.987335
## converged
seas_scons_res2 = sarima(scons_res,2,0,0,1,0,0,7, no.constant = TRUE)
## initial value -2.732810
## iter 2 value -2.878819
## iter 3 value -2.992100
## iter 4 value -3.001923
## iter 5 value -3.003134
## iter 6 value -3.003137
## iter 7 value -3.003137
## iter 7 value -3.003137
## iter 7 value -3.003137
## final value -3.003137
## converged
## initial value -2.987268
## iter 2 value -2.987405
## iter 3 value -2.987408
## iter 4 value -2.987408
## iter 4 value -2.987408
## iter 4 value -2.987408
## final value -2.987408
## converged
seas_scons_res3 = sarima(scons_res,1,0,0,2,0,0,7, no.constant = TRUE)
## initial value -2.737468
## iter 2 value -3.005414
## iter 3 value -3.008169
## iter 4 value -3.008307
## iter 5 value -3.008308
## iter 6 value -3.008309
## iter 6 value -3.008309
## iter 6 value -3.008309
## final value -3.008309
## converged
## initial value -2.990452
## iter 2 value -2.990510
## iter 3 value -2.990513
## iter 4 value -2.990514
## iter 4 value -2.990514
## iter 4 value -2.990514
## final value -2.990514
## converged
seas_scons_res4 = sarima(scons_res,1,0,0,0,0,0,7, no.constant = TRUE)
## initial value -2.731071
## iter 2 value -2.976754
## iter 3 value -2.976883
## iter 4 value -2.976959
## iter 4 value -2.976959
## final value -2.976959
## converged
## initial value -2.964079
## iter 2 value -2.964230
## iter 3 value -2.964257
## iter 4 value -2.964257
## iter 4 value -2.964257
## final value -2.964257
## converged
seas_scons_res1$AIC
## [1] -4.965997
seas_scons_res2$AIC
## [1] -4.960661
seas_scons_res3$AIC
## [1] -4.96718
seas_scons_res4$AIC
## [1] -4.924423
Estimation og valg af SARMA for Produktion
seas_sprod_res1 = sarima(sprod_res,1,0,0,2,0,0,7, no.constant = TRUE)
## initial value -2.031458
## iter 2 value -2.303345
## iter 3 value -2.304909
## iter 4 value -2.310272
## iter 5 value -2.310292
## iter 6 value -2.310301
## iter 7 value -2.310301
## iter 7 value -2.310301
## iter 7 value -2.310301
## final value -2.310301
## converged
## initial value -2.280917
## iter 2 value -2.280944
## iter 3 value -2.280945
## iter 4 value -2.280945
## iter 4 value -2.280945
## iter 4 value -2.280945
## final value -2.280945
## converged
seas_sprod_res2 = sarima(sprod_res,2,0,0,2,0,0,7, no.constant = TRUE)
## initial value -2.031145
## iter 2 value -2.270979
## iter 3 value -2.297740
## iter 4 value -2.308261
## iter 5 value -2.308848
## iter 6 value -2.309075
## iter 7 value -2.309075
## iter 7 value -2.309075
## iter 7 value -2.309075
## final value -2.309075
## converged
## initial value -2.281094
## iter 2 value -2.281176
## iter 3 value -2.281180
## iter 4 value -2.281180
## iter 4 value -2.281180
## iter 4 value -2.281180
## final value -2.281180
## converged
seas_sprod_res3 = sarima(sprod_res,3,0,0,2,0,0,7, no.constant = TRUE)
## initial value -2.029721
## iter 2 value -2.184333
## iter 3 value -2.303575
## iter 4 value -2.315760
## iter 5 value -2.317568
## iter 6 value -2.318229
## iter 7 value -2.318261
## iter 8 value -2.318261
## iter 8 value -2.318261
## iter 8 value -2.318261
## final value -2.318261
## converged
## initial value -2.289435
## iter 2 value -2.289565
## iter 3 value -2.289573
## iter 4 value -2.289575
## iter 5 value -2.289575
## iter 5 value -2.289575
## iter 5 value -2.289575
## final value -2.289575
## converged
seas_sprod_res4 = sarima(sprod_res,0,0,0,2,0,0,7, no.constant = TRUE)
## initial value -2.031748
## iter 2 value -2.088725
## iter 3 value -2.094309
## iter 4 value -2.094449
## iter 5 value -2.094457
## iter 5 value -2.094457
## iter 5 value -2.094457
## final value -2.094457
## converged
## initial value -2.079786
## iter 2 value -2.079795
## iter 3 value -2.079795
## iter 3 value -2.079795
## iter 3 value -2.079795
## final value -2.079795
## converged
seas_sprod_res5 = sarima(sprod_res,1,0,0,1,0,0,7, no.constant = TRUE)
## initial value -2.032823
## iter 2 value -2.265262
## iter 3 value -2.271592
## iter 4 value -2.273270
## iter 5 value -2.273276
## iter 6 value -2.273277
## iter 6 value -2.273277
## final value -2.273277
## converged
## initial value -2.250554
## iter 2 value -2.250598
## iter 3 value -2.250600
## iter 4 value -2.250600
## iter 4 value -2.250600
## iter 4 value -2.250600
## final value -2.250600
## converged
seas_sprod_res6 = sarima(sprod_res,1,0,0,0,0,0,7, no.constant = TRUE)
## initial value -2.033654
## iter 2 value -2.174635
## iter 3 value -2.174745
## iter 4 value -2.174757
## iter 4 value -2.174757
## final value -2.174757
## converged
## initial value -2.159654
## iter 2 value -2.159780
## iter 3 value -2.159789
## iter 3 value -2.159789
## iter 3 value -2.159789
## final value -2.159789
## converged
seas_sprod_res7 = sarima(sprod_res,1,0,0,3,0,0,7, no.constant = TRUE)
## initial value -2.026230
## iter 2 value -2.297344
## iter 3 value -2.301438
## iter 4 value -2.306807
## iter 5 value -2.306896
## iter 6 value -2.306903
## iter 7 value -2.306918
## iter 7 value -2.306918
## iter 7 value -2.306918
## final value -2.306918
## converged
## initial value -2.282058
## iter 2 value -2.282158
## iter 3 value -2.282176
## iter 4 value -2.282180
## iter 5 value -2.282180
## iter 5 value -2.282180
## iter 5 value -2.282180
## final value -2.282180
## converged
seas_sprod_res1$AIC
## [1] -3.553287
seas_sprod_res2$AIC
## [1] -3.548292
seas_sprod_res3$AIC
## [1] -3.559168
seas_sprod_res4$AIC
## [1] -3.151538
seas_sprod_res5$AIC
## [1] -3.49516
seas_sprod_res6$AIC
## [1] -3.314901
seas_sprod_res7$AIC
## [1] -3.550507
SARMA
seas_y1res = ts(seas_sprice_res1$fit$residuals)
coefs_y1 = seas_sprice_res1$fit$coef
coefs_season_Phi_y1 = c(1,rep(0,6),-coefs_y1[2])
stat_y1 = polymult(sprice_res,coefs_season_Phi_y1,1)
seas_x1res = ts(seas_sprod_res3$fit$residuals)
coefs_x1 = seas_sprod_res3$fit$coef
coefs_season_Phi_x1 = c(1,rep(0,6),-coefs_x1[2])
stat_x1 = polymult(sprod_res,coefs_season_Phi_x1,1)
seas_z1res = ts(seas_scons_res3$fit$residuals)
coefs_z1 = seas_scons_res3$fit$coef
coefs_season_Phi_z1 = c(1,rep(0,6),-coefs_z1[2])
stat_z1 = polymult(scons_res,coefs_season_Phi_z1,1)
Opstilling af VAR-model
XXX = data.frame(stat_z1,stat_x1,stat_y1)[8:365,]
var_xx = VAR(XXX, lag.max = 8)
VARselect(XXX)
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 1 8
##
## $criteria
## 1 2 3 4
## AIC(n) -1.130626e+01 -1.131529e+01 -1.140246e+01 -1.138376e+01
## HQ(n) -1.125338e+01 -1.122274e+01 -1.127025e+01 -1.121188e+01
## SC(n) -1.117343e+01 -1.108283e+01 -1.107038e+01 -1.095204e+01
## FPE(n) 1.229569e-05 1.218541e-05 1.116846e-05 1.138002e-05
## 5 6 7 8
## AIC(n) -1.134625e+01 -1.138470e+01 -1.151625e+01 -1.171132e+01
## HQ(n) -1.113471e+01 -1.113351e+01 -1.122539e+01 -1.138080e+01
## SC(n) -1.081491e+01 -1.075374e+01 -1.078566e+01 -1.088111e+01
## FPE(n) 1.181603e-05 1.137175e-05 9.971881e-06 8.206550e-06
## 9 10
## AIC(n) -1.168681e+01 -1.165476e+01
## HQ(n) -1.131662e+01 -1.124491e+01
## SC(n) -1.075697e+01 -1.062529e+01
## FPE(n) 8.412736e-06 8.689992e-06
summary(var_xx)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: stat_z1, stat_x1, stat_y1
## Deterministic variables: const
## Sample size: 350
## Log Likelihood: 636.669
## Roots of the characteristic polynomial:
## 0.9503 0.9503 0.9012 0.9012 0.8972 0.8972 0.8777 0.8777 0.8729 0.8729 0.8428 0.8428 0.8148 0.8148 0.8133 0.8133 0.8107 0.8107 0.8031 0.782 0.782 0.7655 0.7655 0.7362
## Call:
## VAR(y = XXX, lag.max = 8)
##
##
## Estimation results for equation stat_z1:
## ========================================
## stat_z1 = stat_z1.l1 + stat_x1.l1 + stat_y1.l1 + stat_z1.l2 + stat_x1.l2 + stat_y1.l2 + stat_z1.l3 + stat_x1.l3 + stat_y1.l3 + stat_z1.l4 + stat_x1.l4 + stat_y1.l4 + stat_z1.l5 + stat_x1.l5 + stat_y1.l5 + stat_z1.l6 + stat_x1.l6 + stat_y1.l6 + stat_z1.l7 + stat_x1.l7 + stat_y1.l7 + stat_z1.l8 + stat_x1.l8 + stat_y1.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## stat_z1.l1 0.5951356 0.0573602 10.375 < 2e-16 ***
## stat_x1.l1 0.0196595 0.0279328 0.704 0.48205
## stat_y1.l1 -0.0039777 0.0044897 -0.886 0.37629
## stat_z1.l2 0.0760000 0.0662359 1.147 0.25205
## stat_x1.l2 -0.0131725 0.0298994 -0.441 0.65982
## stat_y1.l2 -0.0066493 0.0051514 -1.291 0.19770
## stat_z1.l3 -0.0575799 0.0670678 -0.859 0.39123
## stat_x1.l3 0.0284036 0.0299568 0.948 0.34376
## stat_y1.l3 0.0075568 0.0052586 1.437 0.15167
## stat_z1.l4 -0.0084991 0.0670925 -0.127 0.89927
## stat_x1.l4 0.0234458 0.0300899 0.779 0.43643
## stat_y1.l4 -0.0101087 0.0052842 -1.913 0.05663 .
## stat_z1.l5 0.0134695 0.0665529 0.202 0.83974
## stat_x1.l5 -0.0011361 0.0302069 -0.038 0.97002
## stat_y1.l5 -0.0028914 0.0052850 -0.547 0.58470
## stat_z1.l6 0.0039481 0.0664948 0.059 0.95269
## stat_x1.l6 -0.0260481 0.0304551 -0.855 0.39302
## stat_y1.l6 0.0033576 0.0052542 0.639 0.52326
## stat_z1.l7 -0.1326844 0.0666843 -1.990 0.04746 *
## stat_x1.l7 0.1110872 0.0301637 3.683 0.00027 ***
## stat_y1.l7 -0.0009127 0.0051652 -0.177 0.85985
## stat_z1.l8 0.1557627 0.0568333 2.741 0.00647 **
## stat_x1.l8 -0.0441047 0.0285825 -1.543 0.12379
## stat_y1.l8 -0.0103884 0.0045312 -2.293 0.02251 *
## const 0.0003597 0.0025289 0.142 0.88697
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.04715 on 325 degrees of freedom
## Multiple R-Squared: 0.4727, Adjusted R-squared: 0.4338
## F-statistic: 12.14 on 24 and 325 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation stat_x1:
## ========================================
## stat_x1 = stat_z1.l1 + stat_x1.l1 + stat_y1.l1 + stat_z1.l2 + stat_x1.l2 + stat_y1.l2 + stat_z1.l3 + stat_x1.l3 + stat_y1.l3 + stat_z1.l4 + stat_x1.l4 + stat_y1.l4 + stat_z1.l5 + stat_x1.l5 + stat_y1.l5 + stat_z1.l6 + stat_x1.l6 + stat_y1.l6 + stat_z1.l7 + stat_x1.l7 + stat_y1.l7 + stat_z1.l8 + stat_x1.l8 + stat_y1.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## stat_z1.l1 0.0380076 0.1192246 0.319 0.75009
## stat_x1.l1 0.5428587 0.0580590 9.350 < 2e-16 ***
## stat_y1.l1 0.0023643 0.0093319 0.253 0.80015
## stat_z1.l2 0.4110311 0.1376729 2.986 0.00305 **
## stat_x1.l2 -0.1239843 0.0621466 -1.995 0.04687 *
## stat_y1.l2 -0.0076661 0.0107074 -0.716 0.47453
## stat_z1.l3 -0.2177210 0.1394022 -1.562 0.11930
## stat_x1.l3 0.1559805 0.0622659 2.505 0.01273 *
## stat_y1.l3 0.0113732 0.0109301 1.041 0.29886
## stat_z1.l4 0.2245877 0.1394534 1.610 0.10826
## stat_x1.l4 0.0111100 0.0625426 0.178 0.85912
## stat_y1.l4 -0.0112230 0.0109834 -1.022 0.30763
## stat_z1.l5 0.0327797 0.1383319 0.237 0.81283
## stat_x1.l5 -0.0757495 0.0627859 -1.206 0.22851
## stat_y1.l5 0.0106118 0.0109851 0.966 0.33475
## stat_z1.l6 -0.1475144 0.1382112 -1.067 0.28662
## stat_x1.l6 -0.0321001 0.0633017 -0.507 0.61243
## stat_y1.l6 0.0067477 0.0109209 0.618 0.53709
## stat_z1.l7 0.2933078 0.1386050 2.116 0.03509 *
## stat_x1.l7 0.4440817 0.0626961 7.083 8.78e-12 ***
## stat_y1.l7 0.0009451 0.0107361 0.088 0.92991
## stat_z1.l8 -0.1966949 0.1181295 -1.665 0.09686 .
## stat_x1.l8 -0.3709662 0.0594095 -6.244 1.33e-09 ***
## stat_y1.l8 0.0069602 0.0094182 0.739 0.46043
## const -0.0002448 0.0052563 -0.047 0.96288
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.09799 on 325 degrees of freedom
## Multiple R-Squared: 0.5177, Adjusted R-squared: 0.4821
## F-statistic: 14.54 on 24 and 325 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation stat_y1:
## ========================================
## stat_y1 = stat_z1.l1 + stat_x1.l1 + stat_y1.l1 + stat_z1.l2 + stat_x1.l2 + stat_y1.l2 + stat_z1.l3 + stat_x1.l3 + stat_y1.l3 + stat_z1.l4 + stat_x1.l4 + stat_y1.l4 + stat_z1.l5 + stat_x1.l5 + stat_y1.l5 + stat_z1.l6 + stat_x1.l6 + stat_y1.l6 + stat_z1.l7 + stat_x1.l7 + stat_y1.l7 + stat_z1.l8 + stat_x1.l8 + stat_y1.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## stat_z1.l1 -0.04632 0.78113 -0.059 0.952755
## stat_x1.l1 0.36761 0.38039 0.966 0.334565
## stat_y1.l1 0.62507 0.06114 10.223 < 2e-16 ***
## stat_z1.l2 2.21150 0.90200 2.452 0.014741 *
## stat_x1.l2 -0.15593 0.40717 -0.383 0.701992
## stat_y1.l2 -0.26992 0.07015 -3.848 0.000144 ***
## stat_z1.l3 -2.12668 0.91333 -2.328 0.020499 *
## stat_x1.l3 0.83255 0.40795 2.041 0.042078 *
## stat_y1.l3 0.16771 0.07161 2.342 0.019791 *
## stat_z1.l4 0.62343 0.91367 0.682 0.495508
## stat_x1.l4 -0.36084 0.40976 -0.881 0.379181
## stat_y1.l4 -0.04551 0.07196 -0.632 0.527529
## stat_z1.l5 0.33351 0.90632 0.368 0.713122
## stat_x1.l5 0.11715 0.41136 0.285 0.775980
## stat_y1.l5 -0.03512 0.07197 -0.488 0.625900
## stat_z1.l6 0.54496 0.90553 0.602 0.547720
## stat_x1.l6 -0.47645 0.41474 -1.149 0.251487
## stat_y1.l6 0.07253 0.07155 1.014 0.311492
## stat_z1.l7 -0.22129 0.90811 -0.244 0.807633
## stat_x1.l7 1.57219 0.41077 3.827 0.000155 ***
## stat_y1.l7 0.28227 0.07034 4.013 7.45e-05 ***
## stat_z1.l8 -0.65807 0.77396 -0.850 0.395800
## stat_x1.l8 -0.83627 0.38924 -2.148 0.032415 *
## stat_y1.l8 -0.19753 0.06171 -3.201 0.001504 **
## const -0.01403 0.03444 -0.407 0.684052
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.642 on 325 degrees of freedom
## Multiple R-Squared: 0.5114, Adjusted R-squared: 0.4753
## F-statistic: 14.17 on 24 and 325 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## stat_z1 stat_x1 stat_y1
## stat_z1 0.0022227 0.0009752 0.008576
## stat_x1 0.0009752 0.0096028 0.026390
## stat_y1 0.0085760 0.0263899 0.412208
##
## Correlation matrix of residuals:
## stat_z1 stat_x1 stat_y1
## stat_z1 1.0000 0.2111 0.2833
## stat_x1 0.2111 1.0000 0.4194
## stat_y1 0.2833 0.4194 1.0000
var = restrict(var_xx)
summary(var)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: stat_z1, stat_x1, stat_y1
## Deterministic variables: const
## Sample size: 350
## Log Likelihood: 618.105
## Roots of the characteristic polynomial:
## 0.9468 0.9468 0.9033 0.9033 0.8963 0.8963 0.8924 0.8924 0.8775 0.8775 0.8447 0.8447 0.8169 0.8169 0.7986 0.7986 0.7916 0.7916 0.7853 0.7853 0.7759 0.6891 0.6891 0.4986
## Call:
## VAR(y = XXX, lag.max = 8)
##
##
## Estimation results for equation stat_z1:
## ========================================
## stat_z1 = stat_z1.l1 + stat_y1.l2 + stat_y1.l3 + stat_y1.l4 + stat_z1.l7 + stat_x1.l7 + stat_z1.l8 + stat_y1.l8
##
## Estimate Std. Error t value Pr(>|t|)
## stat_z1.l1 0.605130 0.040448 14.961 < 2e-16 ***
## stat_y1.l2 -0.008347 0.003476 -2.401 0.01686 *
## stat_y1.l3 0.010248 0.003914 2.618 0.00923 **
## stat_y1.l4 -0.010841 0.003402 -3.187 0.00157 **
## stat_z1.l7 -0.116563 0.053594 -2.175 0.03032 *
## stat_x1.l7 0.093560 0.021269 4.399 1.45e-05 ***
## stat_z1.l8 0.145807 0.053462 2.727 0.00671 **
## stat_y1.l8 -0.014068 0.003216 -4.374 1.62e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.04661 on 342 degrees of freedom
## Multiple R-Squared: 0.4582, Adjusted R-squared: 0.4456
## F-statistic: 36.16 on 8 and 342 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation stat_x1:
## ========================================
## stat_x1 = stat_x1.l1 + stat_z1.l2 + stat_x1.l2 + stat_x1.l3 + stat_z1.l7 + stat_x1.l7 + stat_z1.l8 + stat_x1.l8
##
## Estimate Std. Error t value Pr(>|t|)
## stat_x1.l1 0.55284 0.04785 11.554 < 2e-16 ***
## stat_z1.l2 0.33424 0.08844 3.779 0.000185 ***
## stat_x1.l2 -0.14326 0.05051 -2.836 0.004836 **
## stat_x1.l3 0.16129 0.04629 3.484 0.000558 ***
## stat_z1.l7 0.25198 0.11130 2.264 0.024207 *
## stat_x1.l7 0.43684 0.04823 9.058 < 2e-16 ***
## stat_z1.l8 -0.22368 0.11107 -2.014 0.044815 *
## stat_x1.l8 -0.33751 0.05031 -6.709 8.16e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.09707 on 342 degrees of freedom
## Multiple R-Squared: 0.5022, Adjusted R-squared: 0.4905
## F-statistic: 43.13 on 8 and 342 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation stat_y1:
## ========================================
## stat_y1 = stat_y1.l1 + stat_z1.l2 + stat_y1.l2 + stat_y1.l3 + stat_x1.l7 + stat_y1.l7 + stat_x1.l8 + stat_y1.l8
##
## Estimate Std. Error t value Pr(>|t|)
## stat_y1.l1 0.62692 0.05035 12.452 < 2e-16 ***
## stat_z1.l2 1.43554 0.59423 2.416 0.016225 *
## stat_y1.l2 -0.24272 0.05525 -4.393 1.49e-05 ***
## stat_y1.l3 0.15000 0.04731 3.171 0.001658 **
## stat_x1.l7 1.34904 0.35491 3.801 0.000171 ***
## stat_y1.l7 0.32573 0.05543 5.876 9.95e-09 ***
## stat_x1.l8 -0.85976 0.35904 -2.395 0.017175 *
## stat_y1.l8 -0.21285 0.05633 -3.779 0.000186 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.6398 on 342 degrees of freedom
## Multiple R-Squared: 0.4895, Adjusted R-squared: 0.4775
## F-statistic: 40.99 on 8 and 342 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## stat_z1 stat_x1 stat_y1
## stat_z1 0.002286 0.001003 0.009026
## stat_x1 0.001003 0.009915 0.027122
## stat_y1 0.009026 0.027122 0.430602
##
## Correlation matrix of residuals:
## stat_z1 stat_x1 stat_y1
## stat_z1 1.0000 0.2106 0.2877
## stat_x1 0.2106 1.0000 0.4151
## stat_y1 0.2877 0.4151 1.0000
Test af residualerne
roots(var)
## [1] 0.9468395 0.9468395 0.9033093 0.9033093 0.8963237 0.8963237 0.8924446
## [8] 0.8924446 0.8774510 0.8774510 0.8446970 0.8446970 0.8169476 0.8169476
## [15] 0.7986099 0.7986099 0.7915700 0.7915700 0.7852532 0.7852532 0.7759217
## [22] 0.6891159 0.6891159 0.4985940
serial.test(var, type = "BG")
##
## Breusch-Godfrey LM test
##
## data: Residuals of VAR object var
## Chi-squared = 43.21, df = 45, p-value = 0.548
arch.test(var)
##
## ARCH (multivariate)
##
## data: Residuals of VAR object var
## Chi-squared = 203.1, df = 180, p-value = 0.1143
normality.test(var)
## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object var
## Chi-squared = 177.88, df = 6, p-value < 2.2e-16
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object var
## Chi-squared = 43.454, df = 3, p-value = 1.971e-09
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object var
## Chi-squared = 134.42, df = 3, p-value < 2.2e-16
Opstilling af SVAR
amat = diag(3)
diag(amat) = 1
amat[2,1] = NA
amat[3,1] = NA
amat[3,2] = NA
amat
## [,1] [,2] [,3]
## [1,] 1 0 0
## [2,] NA 1 0
## [3,] NA NA 1
svar = SVAR(var, Amat= amat, estmethod = "direct")
summary(svar)
##
## SVAR Estimation Results:
## ========================
##
## Call:
## SVAR(x = var, estmethod = "direct", Amat = amat)
##
## Type: A-model
## Sample size: 350
## Log Likelihood: -1489.885
## Method: direct
## Number of iterations: 196
## Convergence code: 0
##
## LR overidentification test:
##
## LR overidentification
##
## data: XXX
## Chi^2 = 4192, df = 3, p-value <2e-16
##
##
## Estimated A matrix:
## stat_z1 stat_x1 stat_y1
## stat_z1 1.0000 0.000 0
## stat_x1 -0.4376 1.000 0
## stat_y1 -2.8767 -2.444 1
##
## Estimated B matrix:
## stat_z1 stat_x1 stat_y1
## stat_z1 1 0 0
## stat_x1 0 1 0
## stat_y1 0 0 1
##
## Covariance matrix of reduced form residuals (*100):
## stat_z1 stat_x1 stat_y1
## stat_z1 100.00 43.76 394.6
## stat_x1 43.76 119.15 417.1
## stat_y1 394.62 417.09 2254.6
